Nonlinear Dynamics of Colloidal Rotors: Chaos and Order

胶体转子的非线性动力学：混沌与有序

基本信息

批准号：
2108502
负责人：
Petia Vlahovska
金额：
$ 40.5万
依托单位：
Northwestern University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-09-01 至 2024-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2108502&HistoricalAwards=false
关键词：
Nonlinear Dynamics Colloidal Rotors Chaos

项目摘要

Tiny, micron-sized particles called colloids find ubiquitous uses in engineering and biomedical applications, for example, microfluidics and drug delivery, and consumer products, like paint. In recent years, there has been great effort to assemble colloids into new functional materials with designer architecture using electric and magnetic fields. Of particular interest are colloids that spin (rotors), because in such systems the flows stirred by the rotating particles add to the electrostatic interactions thereby vastly expanding the possible structures. This project will study the theory of dynamics of colloids placed between two planar electrodes in order to understand the mechanisms of the field-driven particle assembly. The project integrates knowledge across the fields of applied math, fluid mechanics and soft matter, which will be very beneficial for the training of the students associated with the project. Visually appealing experiments will help educate the public about mathematics and fluid dynamics. This proposal is concerned with a theoretical investigation of the dynamics of rotating colloids powered by the Quincke effect, which is the spontaneous spinning of a dielectric sphere in an applied uniform electric field. The Quincke rotor dynamics in free space is described by the Lorenz equations and the system has gathered attention as one of the physical realizations of Lorenz chaos: at high electric fields the sphere spins irregularly around a fixed axis. However, the dynamics of Quincke rotors in confinement is strikingly different than that in free space. An individual rotor displays three-dimensional motion with periodic reorientation of the axis of rotation. Collectives of hovering Quincke rotors are found to self-organize into stable clusters or snaking chains. This project will investigate the electrohydrodynamics of particles placed between two planar electrodes. The novel mathematical challenges are many and include analytical solutions of single particle dynamics near boundaries, careful consideration of pair-wise hydrodynamic and electrostatic interactions in confinement, and integration of these analytical results into a Stokesian-dynamics-based algorithm for a very large numbers of particles. Benchmark experiments to complement the mathematical research are proposed to justify and validate the mathematical models and to ensure that the research has impact both in and beyond the applied mathematics community. Educational impact includes bringing direct experimental experience in fluid dynamics and soft matter research to applied mathematics undergraduate and graduate students at Northwestern University. The emergent behavior of the Quincke rotors will likely open new research directions across various fields, e.g., non-equilibrium soft matter, materials engineering, and fluid dynamics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

被称为胶体的微小微米级颗粒在工程和生物医学应用中有着广泛的用途，例如微流体和药物输送以及油漆等消费品。近年来，人们在利用电场和磁场将胶体组装成具有设计架构的新型功能材料方面做出了巨大的努力。特别令人感兴趣的是旋转的胶体（转子），因为在这种系统中，旋转粒子搅拌的流动增加了静电相互作用，从而极大地扩展了可能的结构。该项目将研究放置在两个平面电极之间的胶体动力学理论，以了解场驱动粒子组装的机制。该项目整合了应用数学、流体力学和软物质等领域的知识，这对于与该项目相关的学生的培养非常有益。视觉上吸引人的实验将有助于教育公众有关数学和流体动力学的知识。该提案涉及由昆克效应驱动的旋转胶体动力学的理论研究，昆克效应是介电球在施加的均匀电场中的自发旋转。自由空间中的昆克转子动力学由洛伦兹方程描述，该系统作为洛伦兹混沌的物理实现之一而受到关注：在高电场下，球体绕固定轴不规则旋转。然而，限制条件下昆克转子的动力学与自由空间中的动力学截然不同。单个转子显示三维运动以及旋转轴的周期性重新定向。人们发现悬停的昆克转子集体可以自组织成稳定的簇或蛇形链。该项目将研究放置在两个平面电极之间的粒子的电流体动力学。新的数学挑战有很多，包括边界附近的单粒子动力学的解析解，仔细考虑约束中的成对流体动力学和静电相互作用，以及将这些分析结果集成到基于斯托克斯动力学的算法中，用于大量的粒子颗粒。提出了补充数学研究的基准实验，以证明和验证数学模型，并确保该研究对应用数学界内外产生影响。教育影响包括为西北大学应用数学本科生和研究生带来流体动力学和软物质研究的直接实验经验。 Quincke 转子的新兴行为可能会在非平衡软物质、材料工程和流体动力学等各个领域开辟新的研究方向。该奖项反映了 NSF 的法定使命，并通过使用基金会的评估进行评估，认为值得支持。智力价值和更广泛的影响审查标准。